论文标题
受限的Birkhoff多面体和Ehrhart时期崩溃
Restricted Birkhoff polytopes and Ehrhart period collapse
论文作者
论文摘要
我们表明，通过施加额外的不平等，限制“最长增加的子序列”的额外不平等，具有ehrhart quasi-polynomials，即使是诚实的多项式，即使它们只是合理的多面体，也是诚实的多项式。我们通过将连续的，分段线性的两次试验定义到特定的gelfand-tsetlin polytope来做到这一点。该培训不是一个积分的等效性，而是以适当的方式尊重晶格点，以暗示两个多面体具有相同的ehrhart（quasi-）多项式。实际上，两者本质上是罗宾逊·塞格尼斯特·科纳特的对应关系。
We show that the polytopes obtained from the Birkhoff polytope by imposing additional inequalities restricting the "longest increasing subsequence" have Ehrhart quasi-polynomials which are honest polynomials, even though they are just rational polytopes in general. We do this by defining a continuous, piecewise-linear bijection to a certain Gelfand-Tsetlin polytope. This bijection is not an integral equivalence but it respects lattice points in the appropriate way to imply that the two polytopes have the same Ehrhart (quasi-)polynomials. In fact, the bijection is essentially the Robinson-Schensted-Knuth correspondence.
